Contribution to kinematic and inertial analysis of piles by analytical and experimental methods
Contribution to kinematic and inertial analysis of piles by analytical and experimental methods
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通过分析和实验方法对桩的运动学和惯性分析做出贡献
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发表时间：
2013
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通讯作者：
Γεώργιος Ανωγιάτης
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作者：
Γεώργιος Ανωγιάτης
本文从理论分析和试验研究两个方面对桩土相互作用问题进行了研究。地震多发区的桩基会受到直接荷载和间接荷载，前者是由于惯性相互作用而施加在桩头上的轴向力和侧向力，后者是由于运动相互作用而产生的沿着桩身的位移。沿着这条脉络，一族的Tajimi型分析模型的线性弹性动力学理论的框架内，探讨轴向和横向桩土相互作用的影响，在均质和非均质土在静态和动态（运动和惯性）荷载。除了简化的二维模型的Baranov-Novak型，很少有解析解可用于解决这些问题的三维，其中大多数是限制在静态conditions.The建议的模型分析的弹性半空间是基于连续的解决方案开创了日本的调查（特别是Matuso和大原和Tajimi）在20世纪60年代。在这种方法的范围内，土壤被建模为一个连续体，而桩是方便地建模为杆或梁的材料强度理论。位移和应力用土介质固有振型的傅里叶级数表示，土的水平位移对桩的轴向响应和竖向位移对桩的横向响应的影响可以忽略不计。然而，它们对应力的影响是不可忽略的，这将所提出的模型与经典的Tajimi解决方案区分开来，在该解决方案中，上述位移被设置为等于零。上述近似是有吸引力的，因为它们导致运动方程的直接解耦，即使在非均匀介质中，不像经典弹性动力学理论中存在非均匀性时解耦通常是不可能的。尽管近似，所提出的模型优于现有的分析模型和严格的数值方案，因为它们需要相对简单的计算，并且在地震工程和岩土工程中感兴趣的频率范围内提供了对桩响应的良好预测。此外，它们优于现有的Winkler类型的简化分析方法，因为它们更准确，自立，没有经验常数，并提供更真实的问题模拟。与数值方法相比的主要优势（有限元和边界元）的关键在于推导出封闭形式的解，并阐明与动力相互作用现象有关的复杂机制，如辐射阻尼和波在均匀介质中的传播。理论工作的主要目标在于推导出以下问题的封闭形式的解：（i）静态刚度和动态阻抗（动态刚度和阻尼系数）在桩头，（ii）平移和旋转运动响应系数（桩头位移或自由场响应的旋转），（iii）实际的，深度相关的，Winkler模量（弹簧和阻尼系数），（iv）相应的平均，深度无关，温克勒模量，以匹配桩头刚度。此外，为了改进Winkler模型的预测结果，提出了可用于工程实际的Winkler模量的简单近似公式。推导出衰减函数的封闭式表达式，可单独使用或与更精细的方法结合使用，为静态和动态相互作用系数提供更准确的预测，以评估群桩的竖向刚度。新的无量纲频率比控制桩的responses.Finally，新的解决方案添加在分析Winkler模型的上下文中，调查由于垂直传播的S波的运动荷载下的桩的行为。重点讨论了桩身边界条件的影响。参考运动桩弯曲，洞察到物理的问题是通过一个严格的叠加方案，涉及无限长的桩激励运动，和桩的有限长度的集中力和时刻在尖端激发。与经典的弹性动力学理论中桩的响应由六个无量纲比控制相反，在Winkler理论领域中，只有三个无量纲比足以充分描述相互作用问题，并首次引入了机械细长度和有效无量纲频率。文克勒运动学模型的准确性的温克勒模量的选择适当的值进行了论证。理论结果进行了比较，从一系列的试验中获得的新的实验数据进行了缩放模型在振动台上进行的布里斯托大学实验室（BLADE）的框架内的地震工程研究结构（系列）计划，由FP 7，为桩土相互作用的研究做出贡献。
The problem of pile - soil interaction is examined in the Thesis at hand by means of both theoretical analyses and experimental investigations. Pile foundations in seismically prone areas are subjected to both direct loading, such as axial and lateral forces imposed at their heads, resulting from a phenomenon known as inertial interaction, and indirect loading along their body, such as imposed displacements due to the passage of various types of seismic waves, resulting from a phenomenon known as kinematic interaction. Along this vein, a family of analytical models of the Tajimi type are presented in the framework of linear elastodynamic theory to explore the effects of axial and lateral pile - soil interaction in homogeneous and inhomogeneous soil under static and dynamic (kinematic and inertial) loading. Apart from simplified two-dimensional models of the Baranov - Novak type, few analytical solutions are available to tackle these problems in three dimensions, the majority of which are restricted to the analysis of an elastic half space under static conditions.The proposed models are based on a continuum solution pioneered by Japanese investigators (notably Matuso & Ohara and Tajimi) in the 1960’s. In the realm of this approach the soil is modelled as a continuum, while the pile is conveniently modelled as a rod or a beam by strength-of-materials theory. Displacements and stresses are expressed through Fourier series in terms of the natural modes of the soil medium.Fundamental to the analysis presented in this study is that the influence of horizontal soil displacement on axial pile response and vertical displacement on lateral response, respectively, are negligible. However, their effect on stresses is not negligible which differentiates the proposed models from the classical Tajimi solutions in which the aforementioned displacements are set equal to zero. The above approximations are attractive, as they lead to a straightforward uncoupling of the equations of motions, even in inhomogeneous media, unlike the classical elastodynamic theory where the uncoupling is generally impossible in presence of inhomogeneity.Although approximate, the proposed models are advantageous over available analytical models and rigorous numerical schemes, as they require relative simple computations and provide excellent predictions of pile response at the frequency ranges of interest in earthquake engineering and geotechnics. In addition, they are advantageous over existing simplified analytical approaches of the Winkler type, as they are more accurate, self - standing, free of empirical constants and provide more realistic simulation of the problem. The main advantage over numerical methods (finite and boundary elements) lies in the derivation of the solution in closed form and the elucidation of complex mechanisms related to the dynamic interaction phenomenon, such as radiation damping and wave propagation in in homogeneous media.The main goal of the theoretical effort lies in the derivation of solutions in closed - form for: (i) the static stiffness and the dynamic impedances (dynamic stiffness and damping coefficients) at the pile head, (ii) translational and rotational kinematic response factors (pile head displacement or rotation over free-field response), (iii) actual, depth- dependent, Winkler moduli (spring and damping coefficients), (iv) corresponding average, depth- independent, Winkler moduli to match the pile head stiffness. In addition, simple approximate formulae for Winkler moduli to be used in engineering practice are proposed, to improve the predictions of Winkler models.Pile-to-pile interaction is investigated on the basis of the superposition method for axially loaded piles. Closed-form expressions for attenuation functions are derived to be used individually or in conjunction with more elaborate methods providing more accurate predictions for static and dynamic interaction factors to assess the vertical stiffness of pile groups. New dimensionless frequency ratios controlling pile response are introduced.Finally, new solutions are added in the context of analytical Winkler models for investigating the behaviour of piles under kinematic loading due to vertically-propagating S waves. Emphasis is given on the influence of boundary conditions of the pile. With reference to kinematic pile bending, insight into the physics of the problem is gained through a rigorous superposition scheme involving an infinitely-long pile excited kinematically, and a pile of finite length excited by a concentrated force and a moment at the tip. Contrary to the classical elastodynamic theory where pile response is governed by six dimensionless ratios, in the realm of Winkler theory three only ratios suffice to fully describe the interaction problem, from which the mechanical slenderness and the effective dimensionless frequency are introduced for the first time. The selection of an appropriate value for the Winkler modulus in the accuracy of the kinematic Winkler model is demonstrated.The theoretical results are compared to new experimental data obtained from a series of tests on piles carried out on scaled models performed on the shaking table at University of Bristol Laboratory (BLADE) within the framework of the Seismic Engineering Research Infrastructures (SERIES) program, sponsored by FP7, and contribute in the investigation of pile - soil interaction.